The classical local impact laws of Newton and Poisson are able to capture the behaviour observed in single-impact collisions in many situations. However, in the case of collisions with multiple impacts, the simultaneous enforcement of local impact laws does not reproduce essential features of the physical process, such as propagation effects. The aim of this work is to broaden the applicability of the classical Newton impact law to problems involving multiple impacts by assuming instantaneous local impact times and a rigid behaviour of the bodies in contact. The proposed method is implemented as an extension of the nonsmooth generalized-\(\alpha \) method. In order to model events involving multiple impacts, a sequence of impact problems is defined on a vanishing time interval and the active set of each velocity-level sub-problem is redefined in such a way that closed contacts with zero pre-impact velocity are considered inactive. This simple redefinition allows us to deal successfully with many situations involving multiple impacts, by generating a sequence of impact problems which is amenable to be modelled by the simultaneous enforcement of classical impact laws. Additionally, the methodology fits well under the algorithmic structure of the nonsmooth generalized-\(\alpha \) scheme or any scheme dealing with linear complementary problems at velocity level. Several examples are analyzed in order to assess the performance of the method and to discuss its main features.

牛顿和泊松的经典局部撞击定律能够捕获许多情况下单次撞击中观察到的行为。但是，在发生多重碰撞的情况下，同时执行局部碰撞法并不能重现物理过程的基本特征，例如传播效应。这项工作的目的是通过假设瞬时局部碰撞时间和接触物体的刚性行为，将经典牛顿碰撞定律的适用范围扩展到涉及多重碰撞的问题。所提出的方法被实现为非光滑广义- \（\ alpha \）的扩展方法。为了对涉及多个碰撞的事件进行建模，在消失的时间间隔上定义了一系列碰撞问题，并以考虑零碰撞前速度为零的闭合接触的方式重新定义了每个速度水平子问题的有效集。不活跃。这种简单的重新定义使我们能够通过生成一系列影响问题而成功地处理涉及多种影响的许多情况，这些问题可以通过同时执行经典影响定律来建模。此外，该方法非常适合非平滑广义的\（\ alpha \）的算法结构方案或任何在速度水平上处理线性互补问题的方案。分析了几个示例，以评估该方法的性能并讨论其主要功能。